Geometric Shapes and their specification

 

Square

A square is a four sided regular polygon. The circumference of a square with sides of length s is:

The area of a square is:  

Rectangle

The rectangle is a 4 sided polygon, quadrilateral, with right angle corners. The circumference of a rectangle with side lengths of x and y is:

The area of a rectangle is:    

 

Circle

The circle is a shape where all points along the shape are equal distance from a specific point. This point is the center of the circle and the distance to the center of the circle is the radius. The circumference of a circle of radius  is:

The area of a circle is:  

 

Triangle

The triangle is a 3 sided polygon. Triangles can be classified by their sides:

1. Equilateral triangles: All sides are equal in length.
2. Isosceles triangles: Two sides are equal in length.
3. Scalene triangles: All sides have different lengths.

Triangles can also be classified by their angles:

1. Right triangle: One angle is 90 degrees.
2. Oblique triangle: Has no angle equal to 90 degrees.
3. Obtuse triangle: One angle is greater than 90 degrees.
4. Acute triangle: All angles are less than 90 degrees.

The circumference of a triangle is the sum of all sides of the triangle.

The area of a triangle is determined by its base and height.

Parallelogram

A parallelogram is a 4 sided polygon or quadrilateral with two sets of parallel sides. The opposite sides are equal in length. The circumference of a parallelogram is:

The area of a parallelogram is:

Circular Sector

The circular sector is section of a circle enclosed by two radii. The length of the arc of a circular sector, where  is the radii and theta is the angle, is:

The area of the circular sector is:

Circular Ring

The circular ring or donut shape is composed of a circle with a centered small circle removed from the area. The area of a circular ring, where  is the outer diameter and  is the inner diameter, is:

Trapezoid

A trapezoid is a 4 sided polygon or quadrilateral with one set of parallel sides. The circumference of the trapezoid is:

The area of a trapezoid is:

Sphere

The sphere is a 3 dimensional object, whose surface is continuous and all points of the surface are an equal distance from a fixed point, the center. The surface area of a sphere, where  is the radius, is:

The volume of a sphere is:

Cube

A cube is a three dimensional object bounded by 6 equal square sides. The surface area of a cube , where the length of a side is , is:

The volume of a cube is:

Rectangular Box

A rectangular box is a three dimensional object bounded by rectangular or square sides. The surface area of a rectangular box, where the lengths of the sides are , is:

The volume of a rectangular box is:

Cylinder

The cylinder, also know as the right circular cylinder, is formed by rotating a line, of length , around a fixed axis parallel to that line. A cylinder has two ends that are equally sized circles parallel to one another and the circular side is at a right angle to these circular ends. The surface area of cylinder is:

The volume of a cylinder is:

Right Circular Cone

The right circular cone is a three dimensional object created by rotating a right triangle about the vertical side. The surface area of a right circular cone is:

Where the slant height,  is:

The volume of a right circular cone is:

Frustum of a Cone

The frustum of a cone is a portion of cone with the top removed. The top and bottom surfaces are parallel to one another. The volume of a frustum of a cone, where the top radius is    and the bottom radius is , is:

Pythagorean Theorem

The Pythagorean theorem is based upon the right triangle. And If the three sides of the right triangle are , , and  , where   is the hypotenuse, the formula is: